$\int x^{^{\frac34}}\,dx=$ $+C$
The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{^{{\frac34}}}\,dx&=\dfrac{x^{^{{\frac34}+1}}}{{\dfrac34}+1}+C \\\\ &=\dfrac47x^{^{\frac74}}+C \end{aligned}$ In conclusion, $\int x^{^{\frac34}}\,dx=\dfrac47x^{^{\frac74}}+C$